Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma comment(linker, "/stack:247474112")
#pragma GCC optimize("Ofast")
using namespace std;
const long long mod = (long long)1e9 + 7;
const long long infL = 1e18;
int setbit(int n, int pos) { return n = n | (1 << pos); }
int resetbit(int n, int pos) { return n = n & ~(1 << pos); }
bool checkbit(int n, int pos) { return (bool)(n & (1 << pos)); }
template <typename T>
T mul(T x, T y) {
  x %= mod;
  y %= mod;
  return (x * y) % mod;
}
template <typename T>
T add(T x, T y) {
  x %= mod;
  y %= mod;
  return (x + y) % mod;
}
template <typename T>
T modPow(T x, T k, T mod) {
  if (k == 0) return 1;
  if (k & 1) {
    return ((x % mod) * modPow(x, k - 1, mod) % mod) % mod;
  } else {
    T ret = modPow(x, k / 2, mod);
    ret %= mod;
    return (ret * ret) % mod;
  }
}
template <typename T>
T ext_gcd(T num1, T num2, T &X, T &Y) {
  T r2, r1, q2, q1, x2, x1, y2, y1, x, y, r;
  x2 = 1;
  y2 = 0;
  x1 = 0;
  y1 = 1;
  for (r2 = num1, r1 = num2; r1 != 0;
       y2 = y1, y1 = y, x2 = x1, x1 = x, r2 = r1, r1 = r) {
    q1 = r2 / r1;
    x = x2 - q1 * x1;
    y = y2 - q1 * y1;
    r = r2 % r1;
  }
  X = x2;
  Y = y2;
  return r2;
}
template <typename T>
T modInv(T x, T m) {
  return modPow(x, m - 2, m);
}
template <typename T>
void print(const T &v) {
  cerr << v << ' ';
}
template <typename T1, typename... T2>
void print(const T1 &first, const T2 &...rest) {
  print(first);
  print(rest...);
}
template <typename F, typename S>
ostream &operator<<(ostream &os, const pair<F, S> &p) {
  return os << "[ " << p.first << ", " << p.second << " ]";
}
template <typename T>
void trace(T a[], int n) {
  for (int i = 0; i < n; i++) cout << a[i] << ' ';
  cout << "\n";
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  os << "[ ";
  for (int i = 0; i < v.size(); i++) os << v[i] << ' ';
  return os << " ]";
}
template <typename T>
ostream &operator<<(ostream &os, const set<T> &v) {
  os << "[ ";
  for (__typeof((v).begin()) it = (v).begin(); it != (v).end(); ++it)
    os << *it << ' ';
  return os << " ]";
}
const int M = (int)2e6 + 7;
const int mx = (int)700;
struct tt {
  int x, y;
  tt(int a, int b) {
    x = a;
    y = b;
  }
  bool operator<(tt a) const {
    if (x == a.x) return y < a.y;
    return x < a.x;
  }
};
bool cmp(int x, int y) { return x > y; }
int n, a[M + 2], k;
vector<pair<int, int> > v;
void solve() {
  scanf("%d", &n);
  int ans = 1000;
  for (int i = 1; i <= n; i++) {
    int x = n - i;
    if (x < i) ans = min(ans, i);
  }
  for (int i = 1; i <= ans; i++) v.push_back(make_pair(1, i));
  int cnt = 2;
  for (int i = 0; i < (n - ans); i++) v.push_back(make_pair(ans, cnt++));
  cout << ans << "\n";
  for (int i = 0; i < v.size(); i++) {
    cout << v[i].first << ' ' << v[i].second << "\n";
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}